İskandinav ülkelerinin dijital toplum seviyelerinin yeni bir TOPSIS uzantısı ile karşılaştırılması

Abstract

Dijitalleşme, ülkelerin geleceğini belirleyen unsurlardan biridir. Bu nedenle ülkelerin dijitalleşme düzeylerinin karşılaştırılması önemli çok kriterli karar verme (ÇKKV) problemidir. Bu çalışmanın amacı, İskandinav ülkelerinin dijital toplum seviyelerinin objektif bir bakış açısı ile karşılaştırılmasıdır. Bu çalışmanın temel motivasyonu kriter ağırlıklarını içsel olarak belirleyen bir TOPSIS uzantısı ile bu amaca ulaşmaktır. Bu nedenle norm minimizasyonuna dayalı bir TOPSIS uzantısı (NM-TOPSIS) bu çalışmada önerilmiştir. NM-TOPSIS kriterlerin ağırlık vektörünü, alternatiflerin negatif ideal çözüme olan Öklid uzaklıklarının kareleri toplamını minimize edecek şekilde belirler. Başka bir deyişle alternatifleri en kötü durum senaryosu altında karşılaştırır. NM-TOPSIS alternatiflerin öncelik vektörünü, pozitif ideal çözüme uzaklığı minimum yapan ağırlık vektörü olarak belirler. NM-TOPSIS iki farklı konveks kuadratik optimizasyon problemine dayanır. Başka bir deyişle kriterlerin ağırlık vektörü ve alternatiflerin öncelik vektörü belirli bir şart altında tek olarak bulunur. NM-TOPSIS ve güncel OECD verileri kullanılarak yapılan uygulamada, Norveç’in dijital toplum seviyesinin en yüksek olduğu görülmüştür. Aynı kriter ağırlıkları kullanıldığında, TOPSIS sonuçları ve NM-TOPSIS sonuçları arasında yüksek düzeyde pozitif yönlü ilişki olduğu görülmüştür. Öte yandan kriter ağırlıklarındaki değişime bağlı olarak TOPSIS sonuçlarında önemli değişimler vardır.

Keywords

• Çok kriterli karar verme
• Dijitalleşme
• Dijital toplum
• Konveks optimizasyon
• TOPSIS

The comparison of Scandinavian countries’ digital society levels with a novel TOPSIS extension

Abstract

Digitalization is one of the factors that determine the future of countries. Therefore, comparing the digitalization levels of countries is an important multi-criteria decision-making (MCDM) problem. This study aims to compare the digital society levels of Scandinavian countries from an objective perspective. The main motivation of this study is to achieve this aim with a TOPSIS extension that determines criteria weights internally. Thus, a TOPSIS extension based on norm minimization (NM-TOPSIS) is proposed in this study. NM-TOPSIS determines the criteria weight vector in a way that minimizes the sum of squares of the Euclidean distances of alternatives to the negative ideal solution. In other words, it compares alternatives under the worst-case scenario. NM-TOPSIS determines the alternatives’ priority vector as the weight vector that minimizes the distance to the positive ideal solution. NM-TOPSIS depends on two different convex quadratic optimization problems. In other words, the criteria weight vector and the alternatives' priority vector are uniquely found under a certain condition. In the application made using NM-TOPSIS and current OECD data, we see that Norway's digital society level is the highest. When the same criteria weights are used, we observe that there is a high level of positive relationship between TOPSIS results and NM-TOPSIS results. On the other hand, there are significant changes in TOPSIS results depending on the change in criteria weights.

Keywords

• Multi-criteria decision making
• Digitalization
• Digital society
• Convex optimization
• TOPSIS

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